Process for preparing defect free silicon crystals which allows for variability in process conditions

ABSTRACT

A process for growing a single crystal silicon ingot having an axially symmetric region substantially tree of agglomerated intrinsic point defects. The ingot is grown generally in accordance with the Czochralski method; however, the manner by which the ingot is cooled from the temperature of solidification to a temperature which is in excess of about 900° C. is controlled to allow for the diffusion of intrinsic point defects, Such that agglomerated defects do not form in this axially symmetric region. Accordingly, the ratio v/G 0  is allowed to vary axially within this region, due to changes in v or G 0 , between a minimum and maximum value by at least 5%.

BACKGROUND OF THE INVENTION

[0001] The present invention generally relates to the reparation ofsemiconductor grade single crystal silicon which is used in themanufacture of electronic components. More particularly, the presentinvention relates to a process for producing a single crystal siliconingot in which At least a segment of the constant diameter portion ofthe ingot is substantially devoid of agglomerated intrinsic pointdefects, wherein v/G₀ is allowed to vary over the length of the segmentas a result of controlling the manner in which the segment cools to atemperature at which agglomerated intrinsic defects would otherwiseform.

[0002] Single crystal silicon, which is the starting material for mostprocesses for the fabrication of semiconductor electronic components, iscommonly prepared by the so-called Czochralski (“Cz”) method. In thismethod, polycrystalline silicon (“polysilicon”) is charged to a crucibleand melted, a need Crystal is brought into contact with the moltensilicon and a single crystal is grown by slow extraction, Afterformation of a neck is complete, the diameter of the crystal is enlargedby decreasing the pulling rate and/or the melt temperature until thedesired or target diameter is reached. The cylindrical main body of thecrystal which has an approximately constant diameter is then grown bycontrolling the pull rate and the melt temperature while compensatingfor the decreasing melt level. Near the end of the growth process butbefore the crucible is emptied of molten silicon, the crystal diametermust be reduced gradually to form an end-cone. Typically, the end-coneis formed by increasing the crystal pull rate and heat supplied to thecrucible. When the diameter becomes small enough, the crystal is thenseparated from the melt.

[0003] In recent years, it has been recognized that a number of defectsin single crystal silicon form in the crystal growth chamber as thecrystal cools after solidification. Such defects arise, in part, due tothe presence of an excess (i.e., a concentration above the solubilitylimit) of intrinsic point defects in the crystal lattice, which arevacancies and self-interstitials. Silicon crystals grown from a melt aretypically grown with an excess of one or the other type of intrinsicpoint defect, either crystal lattice vacancies (“V”) or siliconself-interstitials (“I”).

[0004] Vacancy-type defects are recognized to be the origin of ouchobservable crystal detects as D-defects, Flow Pattern Defects (FPDs),Gate Oxide Integrity (GOI) Defects Crystal Originated Particle (COP)Defects crystal originated Light Point Defects (LPDs), as well ascertain classes of bulk defects observed by infrared light scatteringtechniques such as Scanning Infrared Microscopy and Laser ScanningTopography. Also present in regions of excess vacancies are defectswhich act as the nuclei for ring oxidation induced stacking faults(OISF). It is speculated that this particular defect is a hightemperature nucleated oxygen agglomerate catalyzed by the presence ofexcess vacancies.

[0005] Defects relating to self-interstitials are less well studied.They are generally regarded as being low densities of interstitial-typedislocation loops or networks. Such defects are not responsible for gateoxide integrity failures, an important wafer performance criterion, butthey are widely recognized to be the cause of other types of devicefailures usually associated with current leakage problems.

[0006] It is believed that the type and initial concentration of thesepoint defects in the silicon are determined as the ingot cools from thetemperature of solidification (i.e., about 1410° C.) to a temperaturegreater than about 1300° C. That is, the type and initial concentrationof these defects are controlled by the ratio v/G₀, where v is the growthvelocity and G₀ is the average axial temperature gradient over thistemperature range. Referring to FIG. 1, for increasing values of v/G₀, atransition from decreasingly self-interstitial dominated growth toincreasingly vacancy dominated growth occurs near a critical value ofv/G₀ which, based upon currently available information, appears to beabout 2.1×10⁻⁵ cm²/sK, where G₀ is determined under conditions in whichthe axial temperature gradient is constant within the temperature rangedefined above. At this critical value, the concentrations of theseintrinsic point defects are at equilibrium. However, as the value ofv/G₀ exceeds the critical value, the concentration of vacanciesincreases. Likewise, as the value of v/G₀ falls below the criticalvalue, the concentration of self-interstitials increases. If theconcentration of vacancies or self-interstitials reaches a level ofcritical supersaturation in the system, and if the mobility of the pointdefects is sufficiently high, a reaction, or an agglomeration event,will likely occur. Under conventional Czochralski-type growthconditions, the density of vacancy and self-interstitial agglomerateddefects is typically within the range of about 1×10³/cm³ to about1×10⁷/cm³. While these values are relatively low, agglomerated intrinsicpoint defects are of rapidly increasing importance to devicemanufacturers and, in fact, are now seen as yield-limiting factors inthe fabrication of complex and highly integrated circuits.

[0007] Preventing the formation of agglomerated intrinsic point defectsmay be achieved by controlling the growth velocity, v, and the averageaxial temperature gradient, G₀, such that the ratio of v/G₀ ismaintained within a very narrow range of values near the critical valueof v/G₀ (see, e.g., FIG. 1, generally represented by range X), thusensuring that the initial concentration of self-interstitials orvacancies does not exceed some critical concentration at Which anagglomeration reaction occurs. However, if control of v/G₀ alone is tohe relied upon in order to prevent the formation of agglomeratedintrinsic point defects, stringent process control and crystal pullerdesign requirements must be met in order to maintain v/G₀ within thisnarrow range.

[0008] Maintaining v/G within a narrow range of values is not the mostcommercially practical approach to preventing the formation ofagglomerated intrinsic point rate is often varied during the growthprocess in order to maintain a constant diameter of the, ingot.Variations in the pull rate, however, result in changes in v which, inturn, impacts v/G₀, causing it to vary axially over the length of theingot. Similarly, changes in G₀ may occur as well, due to changes inother process parameters. Furthermore, it should be noted that G₀ oftenchanges over time as a result of aging of the component of the hot zoneor as a result of the inside of the hot zone becoming coated with, forexample, silicon dioxide.

[0009] The changes in v and G₀likewise cause changes in the “target”range for v/G₀ (i.e., the range which limits the initial concentrationof intrinsic point defects such that agglomeration do not occur), unlessa corresponding and offsetting change is made in G₀ or v, respectively.Therefore, if a given crystal puller is to be utilized to grow a seriesof ingots, the temperature profile of that crystal puller must becontinuously monitored and the process conditions repeatedly modified aschanges in v or C₀ dictate. Such an approach is both time consuming andcostly.

SUMMARY OF THE INVENTION

[0010] Among the several objects and features of the present inventionmay be noted the provision of a process for producing single crystalsilicon, in ingot or wafer form, having an axially symmetric regionwhich is substantially free of agglomerated intrinsic point defects; theprovision of such a process in which a segment of the ingot is allowedto dwell above a temperature at which agglomerated defects wouldotherwise form (i.e., the critical or agglomeration temperature) for atime sufficient to prevent the formation of agglomerated defects withinthe segment; the provision of such a process wherein v/C₀ is allowed tovary axially during ingot growth, as a result of changes in v or G₀;and, the provision of such a process in which the manner by which theingot is cooled between the temperature of solidification and theagglomeration temperature is controlled to prevent the formation ofagglomerated intrinsic point defects.

[0011] Briefly, therefore, the present invention is direction to processfor growing a single crystal silicon ingot having a central axis, aseed-cone, an end-cone, a constant diameter portion between theseed-cone and the end-cone, and an ingot segment which comprises afraction of the constant diameter portion and which is substantiallyfree of agglomerated intrinsic point defects. The process comprises (i)allowing the ratio v/C₀ to vary and a function of the length of theingot segment as the ingot is grown, with v/C₀ being allowed to varybetween a minimum value, (v/G₀)_(min), and a maximum value,(v/G₀)_(max), where v is the growth velocity and G₀ is the average axialtemperature gradient between the temperature of solidification and about1300° C. at the central axis, with (v/G₀)_(min) being no more than about95% of (v/G₀)_(max); and, (ii) cooling the ingot segment from thetemperature of solidification to a temperature between about 1050° C.and about 900° C. over a dwell time, t_(dw), which is sufficient toprevent the formation of agglomerated intrinsic point defects within thesegment.

[0012] The present invention is further directed to a process forgrowing a single crystal silicon ingot having a central axis, aseed-cone, an end-cone, a constant diameter portion between theseed-cone and the end-cone having a circumferential edge and a radiusextending from the central axis to the circumferential edge the ingotbeing characterized in that, after the ingot is grown from a siliconmelt and cooled from the solidification temperature in accordance withthe Czochralski method, the constant diameter portion contains anaxially symmetric region which is substantially free of agglomeratedintrinsic point defect. The process comprises controlling (i) a growthvelocity, v, and an average axial temperature gradient, G₀, during thegrowth of the constant diameter portion of the ingot over a temperaturerange from solidification to about 1300° C.; and, (ii) the cooling rateof the axially symmetric region, the axially symmetric region coolingfrom a first temperature, T₁, which is between about 1400° C. and about1300° C., to a second temperature, T₂, which is between about 1050° C.and about 800° C., with the rate of temperature decrease from T₁ to T₂being controlled such that at each intermediate temperature, T_(lnt)between T₁ and T₂, the axially symmetric region has a concentration ofsilicon self-interstitial intrinsic point defects which is less than acritical concentration at which agglomerated intrinsic point defectsform. The axially symmetric region has a width, as measured radiallyfrom the circumferential edge toward the central axis, which is at leastabout 30% of the width of the constant diameter portion of the ingot andhas a length which is at least about 20% of the length of the constantdiameter portion of the ingot.

[0013] Other objects and features of the present invention will be inpart apparent and in part pointed out hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014]FIG. 1 is a graph which shows an example of how the initialconcentration of self-interstitials, [I], and vacancies, [V], changeswith an increase in the value of the ratio v/G₀, where v is the growthvelocity and G₀ is the average axial temperature gradient.

[0015]FIG. 2 is a graph illustrating the equilibrium concentration andthe critical concentration (i.e., the concentration at whichagglomerated defects forms) as a function of temperature, as furtherdiscussed herein.

[0016]FIG. 3A is a graph of the normalized growth rate as a function ofcrystal length, as described in the Example.

[0017]FIG. 3B is a series of photographs of axial cuts of segments of aningot, ranging from the shoulder to where end-cone growth begins,following copper decoration and a defect-delineating etch, as describedin the Example.

[0018]FIG. 3C is a series of photographs of axial cuts of segments of aningot, ranging from the seed-cone to the end-cone, following copperdecoration and a defect-delineating etch, as described in the Example.

[0019]FIG. 4 is a graph illustrating the relationship between thenormalized concentration of self-interstitial intrinsic point defectsand the normalized growth velocity.

[0020]FIG. 5 is a graph illustrating the relationship between thenormalized concentration of self-interstitial intrinsic point defectsand the normalized growth velocity for various dwell lengths.

[0021]FIG. 6 is a graph illustrating the relationship between variationsin growth velocity (as compared to the critical growth velocity) and thedwell length needed in order to prevent the formation of agglomerateddefects, for various critical growth velocities (for crystal diametersof 200 mm).

[0022]FIG. 7 is a graph illustrating the relationship between variationsin growth velocity (as compared to the critical growth velocity) and thedwell length needed in order to prevent the formation of agglomerateddefects, for various critical growth velocities (for crystal diametersof 150 mm).

[0023]FIG. 8 is a graph illustrating the relationship between variationsin growth velocity (as compared to the critical growth velocity) and thedwell length needed in order to prevent the formation of agglomerateddefects, for various critical growth velocities (for crystal diametersof 300 mm).

[0024]FIG. 9 is a graph illustrating the relationship between thecritical dwell length and the critical growth velocity for ingots ofvarious diameters.

[0025]FIG. 10 is a graph illustrating the relationship between thenormalized concentration of silicon self-interstitials at the criticaltemperature and the ratio of the critical value of G₀ over the actualvalue of G₀, and the impact of changing dwell lengths thereon, for a 150mm diameter single crystal silicon ingot.

[0026]FIG. 11 is a graph illustrating the relationship between thenormalized concentration of silicon self-interstitials at the criticaltemperature and the ratio of the critical value of G₀ over the actualvalue of G₀, and the impact of changing dwell lengths thereon, for a 200mm diameter single crystal silicon ingot.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0027] In accordance with the present invention, it has been discoveredthat controlled cooling may be utilized in the preparation ofsubstantially detect-free silicon to provide sufficient process controlflexibility or robustness, such that v/G₀ may vary or “wander” outsidethe narrow, target range of values that would otherwise have to beemployed to prevent the formation of agglomerated intrinsic pointdefects.

[0028] Control of Growth Conditions

[0029] Previously, it has been reported that process conditions can becontrolled during growth of a single crystal silicon ingot, prepared inaccordance with the Czochralski method, such that the constant diameterportion of the ingot contains a region or segment which is substantiallyfree Of agglomerated Intrinsic point defects. (See, e.g., PCT/US98/07365and PCT/US98/07304.) As disclosed therein, growth conditions, includinggrowth velocity, v, the average axial temperature gradient, G₀, betweenthe temperature of solidification and a temperature greater than about1300° C., and the cooling rate from solidification to about 1050° C.,are controlled to cause the formation of an axially symmetric regionwhich is substantially free of agglomerated intrinsic point defects.

[0030] These growth conditions are preferably controlled to maximize thevolume of this axially symmetric region relative to the volume of theconstant diameter portion of the ingot. When silicon self-interstitialsare the predominant type of intrinsic point defect, the axiallysymmetric region typically has a width equal to at least about 30% ofthe radius of the ingot, with widths of at least about 40%, 60%, 80%,90% and 95% being more preferred. Similarly, when vacancies are thepredominant type of intrinsic point defect, the axially symmetric regionhas a width which is at least about 15 mm. Preferably, however, thisregion Las a width which is equal to at least about 7.5% of the radiusof the ingot, with widths Of at least about 15%, 25% and 50% being morepreferred. Regardless of which intrinsic point defect predominates, mostpreferably the width of the region is about equal to the radius of theingot. Furthermore, this axially symmetric region typically extends overa length of at least about 20% of the constant diameter portion of theingot, with lengths of at least about 40%, 60%, 80%, 90% and even about100% being more preferred.

[0031] As described elsewhere (see, e.g., PCT/US98/07265 andPCT/US98/07304), it is generally believed that the formation of such anaxially symmetric region is achieved as a result of suppressing thereactions in which silicon self-interstitials or crystal lattice vacancyintrinsic point defects react to produce agglomerated intrinsic pointdefects. This suppression is achieved by controlling the concentrationof these intrinsic point defects in this axially symmetric region duringthe growth and cooling of the ingot to ensure this region never becomecritically supersaturated. Preventing critical supersaturation, or theagglomeration of intrinsic point defects, can be achieved byestablishing an initial concentration (controlled by v/G₀(r), where G₀is a function of radius) which is sufficiently low such that criticalsupersaturation is never achieved. However, such an approach requiresthat the actual value of v/G₀ be maintained within a narrow, targetrange of values very close to the critical value of v/G₀.

[0032] Strict process control and system design requirements must becontinuously met if v/G₀(r) is to be maintained within this target rangeof values, because even minor changes in v or G₀may cause the actualvalue of v/G₀ to move outside this range. Stated another way, in theabsence of controlled cooling to provide sufficient dwell time above atemperature at which agglomeration would otherwise occur, and thus allowfor the diffusion of vacancies or interstitials to sinks where they maybe annihilated, v/G₀ must be maintained within this narrow “window” ofvalues over the radius, extending from about the central axis to withina few centimeters (i.e., about 1 to 2 cm) from the circumferential edgeof the ingot. Such process conditions may be expressed by Equation (1):

[(v/G ₀)_(cr) +δ]>v/G ₀(r)>[(v/G ₀)_(cr)−Δ]  (1)

[0033] wherein

[0034] [(v/G₀)_(cr)+δ] is the sum of the critical value for v/G₀ plussome delta, which based on experimental evidence to-date is believed tobe less than about 5% of the critical value, to account for a region ofvacancy dominated material which is substantially free of agglomerateddefects;

[0035] v/G₀(r) is the actual value of v/G₀ at a given radial positionextending from the central axis to within a few centermeters from thecircumferential edge of the ingot; and,

[0036] [(v/G₀)_(cr)−Δ] is the difference between the critical value forv/G₀ minus some delta, which based on experimental evidence to-date isbelieved to be less than about 5% of the critical value, to account fora region of self-interstitial dominated material which is substantiallyfree of agglomerated defects.

[0037] In practice, meeting such stringent process control conditions isdifficult to achieve, and is complicated by the fact that this window ofacceptable values for v/G₀ may change over time in a given crystalpuller. Preferably, therefore, preventing the system from becomingcritically supersaturated, and thus preventing the formation ofagglomerated intrinsic point defects, is achieved by suppressing theinitial concentration of silicon self-interstitials or vacanciessubsequent to crystal solidification, i.e., subsequent to establishingthe initial concentration as determined by v/G₀(r). As noted inPCT/US98/07365 and PCT/US98/07304, it has been found that due to therelatively large mobility of self-interstitials, it is possible toeffectively suppress the concentration of self-interstitials overrelatively large distances, i.e. distances of about 5 cm to about 10 cmor more, by the diffusion of self-interstitials to sinks located at thecrystal surface or to vacancy dominated region located within thecrystal. Diffusion can be effectively used to suppress the concentrationof self-interstitials, provided sufficient time is allowed. In general,the diffusion time will depend upon the radial variation in the initialconcentration of self-interstitials, with lesser radial variationsrequiring shorter diffusion times.

[0038] The amount of self-interstitial diffusion is controlled bycontrolling the time during which the ingot is cooled from thesolidification temperature (about 1410° C.) to the temperature at whichsilicon self-interstitials become immobile, for commercially practicalpurposes. Silicon self-interstitial appear to be extremely mobile attemperatures near the solidification temperature of silicon, i.e. about1410° C. This mobility, however, foregoing the temperature of the singlecrystal silicon ingot decreases. Generally, the diffusion rate ofself-interstitials slows such a considerable degree that they areessentially immobile for commercially practical time periods attemperatures less than about 900° C. However, while the temperature atwhich a golf-interstitial agglomeration reaction occurs may in theoryvary over a wide range of temperatures, as a practical matter this rangeappears to be relatively narrow as a consequence of the relativelynarrow range of initial self-interstitial concentrations which aretypically obtained in silicon grown according to the Czochralski method.In general, therefore, a self-interstitial agglomeration reaction mayoccur, if at all, at temperatures within the range of about 1050° C. toabout 900° C., and typically at a temperature of about 925° C. or about950° C.

[0039] Effects of Diffusion

[0040] Within the range of temperatures at which self-interstitialsappear to be mobiles and depending upon the temperature in the hot zone,the cooling time will typically be controlled ouch that the ingotresides, or “dwells”, within this range for a time which is sufficientto allow enough self-interstitials to diffuse such that criticalsupersaturation does not occur. By controlling this dwell time, t_(dw)the otherwise stringent v/G₀ requirements are relaxed and a larger rangeof v/G₀ values, relative to the critical value, which are acceptable forpurposes of preventing the formation of agglomerated defects areafforded. Such a relationship may be expressed by Equation (2):

[(v/G ₀)+δ]>v/G ₀(r ₀)>[(v/G ₀)_(cr)−Δ(t)_(cr)]  (2)

[0041] wherein

[0042] [(v/G₀)_(cr)+δ] is the same as in Equation (1), above;

[0043] v/G₀(r₀) is the actual value of v/G₀ at about the central axis(given that the diffusion distance is typically the greatest at thispoint); and,

[0044] [(v/G₀)_(cr)−Δ(t)_(cr)] is the difference between the criticalvalue for v/G₀ minus some delta, the delta being a factor of how muchtime a given axial position within the ingot is allowed to dwell abovethe critical temperature (i.e., the temperature at which agglomerationswould otherwise occur).

[0045] It may be observed from Equation (2) that as the dwell timeincreases, there is greater opportunity for the actual value of v/G₀ tovary axially within the segment that is substantially defect-free; thatis, as the dwell time increases, the actual value of v/G₀ may deviatefurther from the target range of values that would otherwise result inthe formation of a substantially defect-free segment of the ingot ifdiffusion was not utilized. Furthermore, it may be observed that thefocus is on v/G₀ near the central axis because the diffusion distance istypically greatest at this point.

[0046] In view of the forgoing and as noted in, for example,PCT/US98/07365 and PCT/US98/07304, typically the axially symmetricregion will be allowed to dwell at a temperature between the temperatureof solidification and a temperature between about 1050° C. and about900° C., and preferably between about 1025° C. about 925° C., for aperiod of (i) at least about 5 hours, preferably at least about 10hours, and more preferably at least about 15 hours for 150 mm nominaldiameter silicon crystals, (ii) at least about 5 hours, preferably atleast about 10 hours, more preferably at least about 20 hours, stillmore preferably at least about 25 hours, and most preferably at leastabout 30 hours for 200 mm nominal diameter silicon crystals, and (iii)at least about 20 hours, preferably at least about 40 hours, morepreferably at least about 60 hours, and most preferably at least about75 hours for silicon crystals having a nominal diameter greater than 200mm. It is to be noted, however, that the precise time and temperature towhich the ingot is cooled is at least in part a function of theconcentration of intrinsic point defects, the number of point defectswhich must be diffused in order to prevent supersaturation andagglomeration from occurring, and the rate at which the given intrinsicpoint defects diffuse (i.e., the diffusively of the intrinsic pointdefects).

[0047] The dwell time, or the manner by which the ingot cools, is atleast in part a function of the growth velocity and the design of thehot zone of the crystal puller; that is, ingot cooling may be affectedby changes in the pull rate and also the configuration of the hot zone,Changes in hot zone configuration can be made using any means currentlyknow in the art for minimizing heat transfer in the hot zone, includingreflectors, radiation shields, purge tubes, light pipes, insulators,heaters and magnetic fields.

[0048] Process Variability

[0049] Controlling the dwell time of a given segment of the constantdiameter portion o˜ the ingot, such that intrinsic point defects maydiffuse to sinks where they are annihilated and thus prevent theformation of agglomerated defects therein, allows the ratio V/G₀ to varyaxially; that is, as a result of controlling the manner by which thissegment of the ingot cools, the ratio v/G₀may change as a function ofthe length of the axially symmetric region, In accordance with thepresent process, therefore, the actual value of the ratio v/G₀ may beallowed to vary as a function of the length of the axially symmetricregion as the ingot is grown between a minimum value, (v/G₀)_(min), anda maximum value, (v/G₀)_(max). In one embodiment of the present process,(v/G₀)_(min) is no more than about 95% of (v/G₀)_(max), while in otherembodiments (v/Go)min is no more than about 90%, 85% or even 80% of(v/G₀)_(max). Stated another way, in one embodiment the actual value ofv/G₀may vary by at least about 5% between (v/G₀)_(min) and (v/G₀)_(max),while in other embodiments v/G₀ may vary between (v/G₀)_(min) and(v/G₀)_(max) by at least about 10%, 15%, 20% or more.

[0050] As used herein and as described in Equation (2) above,(v/G₀)_(max) is intended to refer to (v/G₀)_(cr) plus some delta toaccount for the region of vacancy dominated material which issubstantially free of agglomerated defects. Furthermore, if growthconditions are such that the ingot comprises both vacancy andinterstitial dominated material which are substantially free ofagglomerated defects, then (v/G₀)_(max) is intended to refer to[(v/G₀)_(cr)+δ(t)_(cr)] which, as further discussed below in referenceto Equation 3, represents the sum of the critical value of v/G₀ plussome delta which is a factor of how much time a given axial positionwithin the ingot is allowed to dwell above the critical temperature(i.e., the temperature at which agglomerations would otherwise occur).

[0051] It is to be noted that the above ranges for axial variations inthe ratio v/G₀ refer to the values of v/G₀ within the axially symmetricregion of the ingot which is substantially free of agglomeratedintrinsic point defects. Furthermore, v/G₀ may also vary radially(v/G₀(r)). It is therefore to be understood that (V/G₀)_(min) and(V/G₀)_(max) generally refer to the minimum and maximum values forv/G₀(r), respectively, within the axially symmetric region. However,when growth conditions are controlled such that the axially symmetricregion extends from the central axis to the circumferential edge of theingot, variations in v/G₀ are typically determined based on the value ofv/G₀ at the central axis because the diffusion distance is greatest atthis position, provided there is little or no contribution from axialdiffusion.

[0052] It is also to be noted that, as further described in detail belowin reference to FIGS. 4 and 5, when the variations in v/G₀ are due tochanges in v (i.e., G₀ is constant), the axial variations in v/G₀ may besignificantly greater; that is, when interstitials predominate and whenvariations in v/G₀ are due to changes in v, (v/G₀)_(min) may be no morethan about 60%, 40%, 20%, 10% or even 5% of (v/G₀)_(max). In otherwords, provided there is sufficient dwell time, the “window” ofacceptable values for v/G₀ may essentially be any value less than thecritical value for v/G₀. Experience to-date suggests an illustrated inFIG. 5, once the dwell time is sufficient for v/G₀ to vary by about 20%(i.e., when (V/G₀)_(min) is no more than about 80% of (v/G₀)_(max)),(v/G₀)_(min) may essentially be any value less than (v/G₀)_(max).

[0053] While v/G₀ may vary as described above when G₀ is constant and vis allowed to change, it is to be noted that v/G₀ may also vary when vis constant and G₀ is allowed to change. More specifically, as furtherdescribed in detail below in reference to FIGS. 10 and 11, theacceptable degree of variation in v/G₀ resulting from changes in G₀increases as the dwell time increases. However, as FIGS. 10 and 11indicate, the “window” of acceptable values for v/G₀ when v is constantand G₀ is allowed to vary does not have a dwell time plateau where thiswindow of values becomes essentially wide open, allowing for any valueless than the critical value for v/G₀. Rather, the degree of acceptablevariation (i.e., variation in v/G₀ which may occur without the formationof agglomerated defects) continues to increase as the dwell timeincreases.

[0054] As discussed above, by allowing the axially symmetric region todwell above about 900° C. for an extended period of time, the otherwisestringent v/G₀ requirements are relaxed and a larger range of v/G₀values, relative to the critical value, are acceptable for purposes ofpreventing the formation of agglomerated intrinsic point defects andgrowing a single crystal silicon ingot is described herein. For example,if the width of the axially symmetric region in which interstitials arethe predominant intrinsic point defect is to be about equal to theradius of the ingot, then the growth velocity, v, and the average axialtemperature gradient, G₀, (as previously defined) may be controlled suchthat the ratio v/G₀ is between about 0.75 to about 1 times the criticalvalue of v/G₀ (i.e., about 1.6×10⁻⁵ cm²/sK to about 2.1×10⁻⁵ cm²/sKbased upon currently available information for the critical value ofv/G₀). Typically, however, in view of the flexibility provided by thepresent process, the ratio v/G₀ may range in value from about 0.6 toabout 1 times the critical value of v/G₀ (i.e., about 1.3×10⁻⁵ cm²/sK toabout 2.1×10⁻⁵ cm²/sK based upon currently available information for thecritical value of v/G₀), and preferably from about 0.5 to about 1.05times the critical value of v/G₀ (i.e., about 1×10⁻⁵ cm²/sK to about2.2×10⁻⁵ cm²/sK based upon currently available information for thecritical value of v/G₀). Most preferably, however, the dwell time willbe controlled such that the ratio v/G₀ may have any value less thanabout 1.05 times the critical value of v/G₀.

[0055] It should be noted that the precise range of acceptable valuesfor v/G₀ is at least partially dependent upon the desired width of theaxially symmetric region to be obtained. Accordingly, while the aboveranges exhibit the flexibility of the present process when the width ofthis region is about equal to the width of the constant diameter portionof the ingot, this flexibility is even greater when it is acceptable forthe width of this region to be less than the radius of the ingot. Insuch instances the growth velocity, v, and the average axial temperaturegradient, G₀, may be controlled such that the ratio v/G₀ ranges in valuefrom about 0.6 to about 1.5 times the critical value of v/G₀ (i.e.,about 1.3×10⁻⁵ cm ²/sK to about 3×10⁻⁵ cm²/sK based upon currentlyavailable information for the critical value of v/G₀), and preferablyfrom about 0.5 to about 2.5 times the critical value of v/G₀ (i.e.,about 1×10⁻⁵ cm²/sK to about 5×10⁻⁵ cm²/sK based upon currentlyavailable information for the critical value of v/G₀). Strictlyspeaking, however, when the only goal is the formation of an axiallysymmetric region of interstitial dominated material of some minimumradial width (i.e., at least about 30%, 40%, 80% or more of the constantdiameter portion), then v/G₀ may be essentially any value greater thanthe critical value, provided that at some position along the radius thevalue falls below that value which is need to result in the formationthis axially symmetric region of the desired width.

[0056] It Should be further noted that, given a dwell time which is longenough to allow for sufficient vacancy diffusion, an axially symmetricregion of vacancy dominated material may also be formed. If the width ofthis region is to be about equal to the radius of the constant diameterportion of the ingot, v/G₀ may range from about 0.95 to about 1.1 timeshe critical value of v/G₀. However, as pointed about above withreference to an interstitial dominated region, if the width of thisvacancy dominated region is less than the radius of the ingot, greatervariations in v/G₀ are acceptable.

[0057] The above-noted ratios of v/G₀ may be achieved by the independentcontrol of the growth velocity, v, and the radial variations in theaverage axial temperature gradient, G₀(r). While a single value of v/G₀within the range may be achieved during the growth process by carefulcontrol of the growth velocity and design of the crystal Duller hotzone, preferably v/G₀ will be allowed to vary within the noted rangeduring the growth of the axially symmetric region such variation mayresult from (i) allowing the growth velocity to vary during growth in acrystal puller hot zone designed in such a way that G₀ is essentiallyconstant over the radius and length of the region (ii) maintaining aconstant growth velocity while G₀ is allowed to vary, or (iii) allowingboth v and G₀ to vary.

[0058] Prior to the present invention, a conflict has existed betweencontrolling v/G₀ to prevent the formation of agglomerated defects andcontrolling process conditions for conventional growth purposes, such asto maintain a constant diameter off the ingot main body or grow theend-cone. This conflict has meant that if agglomerated defects are to beprevented, this prevention must be achieved at some cost. However, inaccordance with the present process, v/G₀ is allowed to vary, whichmeans in one embodiment the pull rate may also vary, in order forexample to maintain diameter control. Accordingly, as an example, thepull rate after about one diameter of the crystal length may range fromabout 0.3 mm/minute to about 0.5 mm/minute, from about 0.25 mm/minute toabout 0.6 mm/minute, or from about 0.2 mm/minute to about 0.8 mm/minute,the range of acceptable pull rates increasing as the process flexibilityincreases.

[0059] It is to be noted that the pull rate is dependent upon both thecrystal diameter and crystal puller design. The stated ranges aretypical for 200 mm diameter crystals. In general, the pull rate willdecrease as the crystal diameter increases. However, the crystal pullermay be designed to allow pull rates in excess of those stated here. As aresult, most preferably the crystal puller will be designed to enablethe pull rate to be as fast as possible, and thus allow v/G₀ to vary asmuch as possible, while still prevent the formation of agglomeratedintrinsic point defects.

[0060] In addition to allowing for variations in the pull rate, or moregenerally variations in v, the flexibility of the present process alsoallows for G₀ to vary or drift. More specifically, because v/G₀ isallowed to vary, the present process is more robust, thus allowing forthese variations to occur regardless of the cause; that is, the robustnature of the present process allows for variations in v/G₀ to occurwhen G₀ is constant and v varies, when v is constant and G₀ varies, orwhen both vary. For example, the present process affords the means bywhich to prepare, in a given crystal puller, a series of single crystalsilicon ingots in which the formation of agglomerated intrinsic pointdefects invented and wherein both the pull rate and G₀ may drift duringtheir preparation. As a result, the need to maintain a constant pullrate (at the cost of diameter control), as well as the need tocontinuously monitor the temperature profile for the given crystalpuller hot zone and make adjustments in the process conditions as thehot zone parts age (thus causing G₀ to drift), are eliminated.

[0061] By taking advantage of self-interstitial or vacancy diffusionthrough controlling the dwell time, the present process effectivelycreates a larger “window” of v/G₀ values which can be utilized toobtained an axially symmetric region of the constant diameter portion ofthe ingot which is substantially free of agglomerated intrinsic pointdefects. It is to be noted however, that increasing the window size (orallowable v or G₀ variations for defect-free growth) is substantiallylimited to those values of v and G₀ which result in values for the ratiov/G₀ which are smaller than the critical v/G₀ value. Stated another way,the effect is strongest for interstitial dominated material becausesilicon self-interstitials diffuse more quickly than vacancies. As aresult, the window opens more quickly toward lower values for v/G₀. Forexample, increasing for the window size for allowable pull ratevariations is substantially limited to slower pull rates because, due tothe diffusively of interstitials, the window opens more quickly towardthese lower pull rates.

[0062] In principle, however, as the time the ingot spends attemperatures greater than about 900° C. increases, the window forallowable v/G₀ variations due to v/G₀ values greater than the criticalvalue of v/G₀ plus some small delta (resulting from, for example,variations toward faster pull rates) also increases; that is, as thedwell time increases, in principle the window of acceptable v/G₀ valuesfor vacancy dominated material also increases because greater time isallowed for vacancies to diffuse. Such a relationship can be expressedby Equation (3):

[(v/G ₀)_(cr)+δ(t)_(cr) ]>v/G ₀(r₀)>[(v/G ₀)_(cr)−Δ(t)_(cr)]  (3)

[0063] wherein

[0064] [(v/G₀)_(cr)+δ(t)_(cr)] is the sum of the critical value for v/G₀plus some delta, the delta being a factor of how much time a given axialposition within the ingot is allowed to dwell above the criticaltemperature (i.e., the temperature at which agglomerations wouldotherwise occur)

[0065] v/G₀(r₀) is the same as in Equation (2), above; and,

[0066] [(v/G₀)_(cr)−Δ(t)_(cr)] is the same as in Equation (2), above.

[0067] As can be seen from the expression [(v/G₀)_(cr)+δ(t)_(cr)],as thedwell time increases, so the range of values for v/G₀ above the criticalvalue also increases. However, due to the slower diffusion rate ofvacancies, the formation of an axially symmetric region of vacancydominated material which is substantially free of agglomerated intrinsicpoint defects would require significantly longer times for diffusion,particularly given that this region extends from the central axis to thecircumferential edge of the constant diameter portion of the ingot.

[0068] “Local” Cooling Rate

[0069] In addition to controlling time during which the ingot dwellswithin the noted range, it is also preferred to control the rate atwhich the ingot cools within this range and over this time period.Stated another way, while it is preferred to maintain the ingot abovethe temperature at which agglomerated defects will form for a period oftime, it is also preferred to control the “local” (in time) coolingrate, that is, the rate at which the ingot cools within this time andtemperature range. For example, referring now to FIG. 2, it may beobserved that for each local temperature within the range bounded by thesolidification temperature, and more specifically the temperature atwhich the initial concentration of intrinsic point defects isestablished (i.e., some temperature between about 1400° C. and about1300° C.) and the temperature at which intrinsic point defects are nolonger sufficiently mobile for agglomerations to occur (i.e., sometemperature greater than about 900° C.), there exists an equilibriumconcentration C_(eq) and a critical or nucleation concentration C_(n)where a reaction or agglomeration occurs. Accordingly, for a givenconcentration (denoted point A) above the equilibrium concentration butbelow the critical concentration, if sufficient time is spent at asingle temperature above the temperature of agglomeration, eventuallyenough interstitials will out-diffuse such that the equilibriumconcentration is reached (denoted point B) However, if the temperatureis then rapidly reduced, an agglomeration may still occur (denoted pointD). As a result, to ensure sufficient time for out-diffusion it ispreferred that a given axial position in the growing ingot (denotedpoint A) remain above the temperature of agglomeration for the requisitetime, but in addition that it be cooled at a rate which prevents thecritical concentration from being exceeded (see, e.g., path denoted E).

[0070] It is also to be noted from FIG. 2 that experience to-datesuggests that the concentration of interstitials as given temperature(i.e., C(T)), between the reaction or nucleation temperature and theequilibrium temperature or that concentration, decrease much glower thanthe corresponding equilibrium concentration (i.e., C_(eq)(T)); that is,experience to-date suggests that C(T) decreases much slower than C_(eq).As a result, as the temperature decreases, C moves away from C_(eq) andtoward the nucleation concentration, C_(n), which means it the ingotcools too fast eventually the curve C(T) will intersect with C_(n)(T)and thus an agglomeration event will occur. Accordingly, it should benoted that while a high cooling rate may be acceptable at higher ingottemperatures, as the ingot cools the rate will preferably decrease toensure nucleation, and thus agglomeration, do not occur. It should befurther noted, however, that the temperature at which C(T) intersectswith C_(n)(T) is at least in part a function of the initial defectconcentration and the rate

[0071] at which the defects diffuse through the crystal lattice of theingot.

[0072] In accordance with the present process, therefore, the manner inwhich the ingot cools within the range of temperatures in whichself-interstitials, or alternatively vacancies, appear to be mobile iscontrolled such that the ingot cools from a first temperature, T₁, to asecond temperature, T₂, with the rate of temperature decrease from T₁ toT₂ being controlled much that at each intermediate temperature, T_(lnt),between T₁ and T₂ the axially symmetric region has a concentration ofintrinsic point defects which is less than the critical concentration atwhich agglomerated intrinsic point defects will form. The firsttemperature, To, is typically between about 1400° C. and about 1300° C.,preferably between about 1350° C. and about 1310° C. The secondtemperature, T₂, is typically between about 1050° C. and about 800° C.,preferably between about 1000° C. and about 900° C., and most preferablybetween about 975° C. and about 925° C.

[0073] Referring again to FIG. 2, it is to be noted that typically therate at which the axially symmetric region of the ingot cools between T₁and T₂ will be controlled such that, any given temperature, the actualconcentration of self-interstitials, or vacancies, remains below theconcentration at which agglomeration will occur but well above theequilibrium concentration in order to ensure the greatest rate ofdiffusion possible. For example, the rate may be controlled such that ata given axial position the actual concentration of intrinsic pointdefects within the axially symmetric region can be expressed as inEquation (4):

C=C _(eq) +X(C _(n) −C _(equil))  (4)

[0074] wherein

[0075] C is the actual concentration of intrinsic point defects at thegiven axial position;

[0076] C_(eq) is the equilibrium concentration of intrinsic pointdefects for this axial position;

[0077] X is a constant, typically ranging from about 0.4 to less thanabout 1, and preferably from about 0.6 to about 0.9; and,

[0078] C_(n) is the concentration of intrinsic point defects which issufficient to cause an agglomeration reaction to occur at this axialposition.

[0079] It is to be noted that, while it is generally preferred that thecrystal growth conditions be controlled to maximize the width of theinterstitial dominated region, there may be limits for a given crystalpuller hot zone design. As the V/I boundary in moved closer to thecentral crystal axis, provided the cooling conditions and G₀(r) do notchange, the minimum amount Of radial diffusion required increases. Inthese circumstances, there may be a minimum radius of the vacancydominated region which is required to suppress the formation ofagglomerated interstitial defects by radial diffusion.

[0080] It is to be further noted that, in order to achieve the effectsof controlling the cooling rate and dwell time over appreciable lengthsof the constant diameter portion of the ingot, consideration must alsobe given to the growth process of the end-cone of the ingot, as well dothe treatment of the ingot once end-cone growth is complete, to ensurethat the latter portion of the main body of the ingot generally hag thegame thermal history as the portions which preceded it. Severalapproaches to dealing with this situation are discussed in all in, forexample, PCT/US98/07365 and PCT/US98/07304.

[0081] It is also to be noted that, as crystal puller and hot zonedesigns vary, the ranges presented above for v/G₀, pull rate, coolingtime and cooling rate may also vary.

[0082] For an ingot prepared in accordance with the process of thepresent invention and having a V/I boundary, i.e. an ingot containingmaterial which is vacancy dominated, experience has shown that lowoxygen content material, i.e., less than about 13 PPMA (parts permillion atomic, ASTM standard F-121-83), is preferred. More preferably,the single crystal silicon contains less than about 12 PPMA oxygen,still more preferably less than about 11 PPMA oxygen, and mostpreferably less than about 10 PPMA oxygen. This is because, in medium tohigh oxygen contents wafers, i.e., 14 PPMA to 18 PPMA, the formation ofoxygen-induced stacking faults and bands of enhanced oxygen clusteringjust inside the V/I boundary becomes more pronounced. Each of these area potential source for problems in a given integrated circuitfabrication process. However, it is to be noted that, when the axiallysymmetric region has a width about equal to the radius of the ingot, theoxygen content restriction is removed; this is because, given that novacancy type material is present, the formation of such faults andclusters will not occur.

[0083] Process/System Design

[0084] As previously discussed, the type and initial concentration ofintrinsic point defects within the growing single crystal silicon ingotare a function of the actual value of the ratio of v/G₀ relative to thecritical value of v/G₀. The critical growth velocity, v_(cr), may beexpress as in Equation (5):

v _(cr) =ξG ₀  (5)

[0085] wherein

[0086] C₀ is the average axial temperature gradient; and,

[0087] ξ represents the critical value, which is currently believed tobe about 2.1×10⁻⁵ cm²/sK.

[0088] If G₀ is constant over the radius of the ingot, then the type andinitial concentration of these defects are primarily a function of v;that is, the type and initial concentration of intrinsic point defectsmay be expressed in terms of the ratio v/v_(cr). Accordingly, if thegrowth velocity v is greater than v_(cr) then vacancies are predominant,while if v is less than v_(cr) self-interstitials are predominant.

[0089] A relationship exists between the growth velocity, the time theingot dwells above the agglomeration temperature and the distance overwhich a given axial position travels as the ingot cools from near thesolidification temperature to the agglomeration temperature, such thatthe formation of agglomerated intrinsic point defects is prevented. Therelationship between this distance, or “dwell length” (L_(dw)), thegrowth velocity and the dwell time is expressed in Equation (6) asfollows:

t=L _(dw) /v.  (6)

[0090] It is to be noted that the temperature profile is believed to bealmost unaffected by variations in v, such that L_(dw) may be consideredas a constant for a given hot zone.

[0091] Solving the problem of silicon self-interstitial diffusion in asingle crystal silicon ingot, by means commonly known in the art,additionally leads to the conclusion that, when G₀ is constant, therelationship between L_(dw), a given growth velocity less than or equalto the critical velocity and the concentration of self-interstitials(relative to the melting point equilibrium concentration C_(m); i.e.,the concentration of self-interstitials at the time of solidification)may be expressed as in Equation (7):

C/C _(m)=1.602B (1−v/v _(cr)) exp (μ−L _(dw))  7)

[0092] wherein

[0093] C/C_(m) is the “normalized” concentration (i.e., theconcentration of self-interstitials relative to the concentration at thetime of solidification);

[0094] B is a proportionality coefficient which is dependent upon theassumed point defect parameters; a reasonable estimate is about 0.5;

[0095] v/v_(cr) is the actual growth velocity relative to the criticalgrowth velocity;

[0096] μ is a decay coefficient which, for the typical growth parametersof common Cz-type silicon wherein the contribution of axial diffusion issmall, may be expressed as equal to (D/v) (λ₁/R)², wherein D is thediffusively of self-interstitials, v is the growth velocity, λ₁ is thefirst root of the Bessel function, J₀(λ₁)=0 and is equal to about 2.40and R is the radius.

[0097] Based upon experimental evidence to-date, it is generallybelieved that at a temperature of about 900° C. to about 925° C., theformation of agglomerated defects can be avoided if the value of theratio C/C_(m) is less than about 0.01, and preferably less than about0.005. Using these values and Equation (7), the degree of variabilitythat is acceptable (i.e., the degree of variability a given system canhave and still yield a substantially defect-free axially symmetricregion of a width essentially equal to the radius of the ingot) for agiven dwell length can be determined alternatively, using these valuesand the known or desired variability in a given crystal pulling process,a dwell length can be determined which is sufficient to yield asubstantially defect-free axially symmetric region of a wall toessentially equal to the radius of the ingot. In other words, given thatsome variation in process conditions is to be expected, the relationshipprovided in Equation (7) may be used to provide the details needed todesign a robust process; that is, Equation (7) may be used to design asystem which is capable of coping with expected process variations andstill enable the growth of substantially defect-free silicon.

[0098] Referring now to FIG. 4, it may be observed that for a givendwell length, the normalized concentration increases as the actualvelocity, relative to the critical velocity, (i.e., v/v_(cr)) decreasesuntil the growth velocity become so slow that sufficient lime is allowedfor self-interstitials to out-diffusion, effectively lowering theoverall concentration. Experimental evidence to date suggests that forthe particular process conditions and system represented (i.e.,v_(cr)=0.28 mm/min.; ingot radius=100 mm; L_(dw) 690 mm) the relativecritical concentration which, if exceeded, results in the formation ofagglomerated intrinsic point defects, is believed to be about 0.01,while in some instances it may be about 0.005 or less. Accordingly, itmay be observed that the actual growth velocity must be very close, orvery far away from, the critical velocity if the formation ofagglomerated intrinsic point detects is to be prevented; that is, inthis instance there are two “windows” for v/G₀ which enable theformation of agglomerated defects to be avoided, one very near to thecritical value and one far away from it. Referring now to FIG. 5, it canbe seen that as L_(dw), increases for a given growth velocity, thecorresponding relative concentration of silicon self-interstitialsdecrease (where curves 1-7 correspond, respectively, to dwell lengths of400 mm, 500 mm, 600 mm, 700 mm, 800 mm, 900 mm and 980 mm).

[0099] Increasing L_(dw) effectively extends the range of actual growthvelocities which are acceptable for purposes of growing a single crystalsilicon ingot which is substantially free of agglomerated defects. AsL_(dw) continues to increase, eventually this “window” of acceptablegrowth velocities extends over the entire range (see, e.g., FIG. 5,curve 7); that is, L_(dw) eventually reaches a critical value at whichC<C_(cr) at any v<v_(cr). It can be seen that for the present example,the critical value for L_(dw) is about 980 mm, which is comparable tothe typical length of a Cz-type single crystal silicon ingot. Therefore,to prevent the formation of agglomerated defects over the entire usablelength of the crystal, the pulling of the ingot must continue at thesame even after growth is complete in order to ensure sufficient dwelltime (unless the ingot is prepared following an alternative growthprocess, such as by holding the ingot in the pull chamber after growthis complete with while maintaining, and then slowly cooling, the ingotusing pull chamber “after” heaters).

[0100] Referring now to FIGS. 6-8, the dependence of this window ofacceptable growth velocities on L_(dw) is further illustrated. Thesecurves may be used to determine the dwell length needed in order toobtain substantially defect-free silicon in view of the known or desiredvariability in a given set of process conditions. Stated another way,given that each crystal puller hot zone has an inherent critical G₀ and,as such, has a corresponding v_(cr), once the amount of variability in agiven process is determined, or a desired variability is established,this ratio of v/v_(cr) can be used in conjunction with the graphspresent in FIGS. 6-8 to generally determine the dwell length needed toprevent the formation of agglomerated defects.

[0101] As an example, if a 200 mm diameter ingot is to be grown (see,e.g., FIG. 6) in a crystal puller have a thermal profile such thatv_(cr) is about 0.28 mm/minute (i.e., curve 3) and the desiredvariability is about 20%, then a single crystal silicon ingot may begrown, the entire usable length of which is substantially free ofagglomerated defects, if the L_(dw) is about 100 cm in length. Statedanother way, such an ingot can be grown if, by employing upper heatersand reflector for example, the hot zone is design to that each axialposition of the constant diameter portion of the ingot travels about 100cm while cooling from about the temperature of solidification to thecritical temperature at which agglomerations would otherwise form.

[0102] It is to be noted, in regard to FIGS. 6-8, which correspond toingot diameters of 200 mm, 150 mm and 300 mm, respectively, that dwelllengths are provided for a number of different v_(cr) values, the curvesin each graph corresponding to the v_(cr) values as given below in TableI: TABLE I Curve V_(cr) (FIG. 6) V_(cr) (FIG. 7) V_(cr) (FIG. 8) 1 0.15mm/min 0.25 mm/min 0.10 mm/min 2 0.25 mm/min 0.35 mm/min 0.15 mm/min 30.28 mm/min 0.45 mm/min 0.20 mm/min 4 0.35 mm/min 0.55 mm/min 0.25mm/min 5  0.4 mm/min — — 6 0.55 mm/min — —

[0103] Referring again to FIG. 5, it can be observed that if the dwelllength is sufficiently great, the actual growth velocity may be anyvalue less than about the critical value, in order grow a single crystalsilicon ingot of interstitial dominated material which is substantiallyfree of agglomerated defects. More specifically, it may be observed fromcurve 7 that as L_(dw) approaches about 970 mm, which in this example isthe critical length (L_(cr)), the “window” for variations in the v, andthus v/G₀, is essential completely open; that is, if L_(dw) is about 970mm, then all values less than about v_(cr), and thus all values of v/G₀less than the critical value of v/G₀ plus some, delta to allow for theannihilation of vacancies by recombination (given that Go is assumed tohe essentially constant here), will enable the growth ofinterstitial-dominated single crystal silicon which is substantiallydefect-free.

[0104] The dependence of the critical value of L_(dw), on v_(cr) may befurther illustrated by Equation (8) to wherein all units are mm andminutes):

L _(cr)=0.35v _(cr) R ²  (8)

[0105] wherein

[0106] L_(cr) is the critical value for L_(dw); that is, the lengthwhich is sufficient to allow v to be any value less that v_(cr) andstill prevent the formation of agglomerated defects;

[0107] v_(cr) is the critical value for the growth velocity (mm/minute),as described above; and,

[0108] R is the radius of the ingot being grown.

[0109] The relationship between the critical length for L_(dw) and thecritical growth velocity v_(cr) is further illustrated by FIG. 9 foringot diameters of 150 mm, 200 mm and 300 mm (curves 1, 2 and 3,respectively). More specifically, the graph presented in FIG. 9 showsthe relationship between v_(cr) when the “window” of acceptablevariations is completely open (i.e. any variation for interstitialdominated growth is acceptable) and the corresponding L_(dw) needed inorder to obtain an ingot which is substantially defect-free overessentially the entire usable length.

[0110] It is to be noted that while the above expression is for purposedof describing the relationship between the critical value for L_(dw),the growth velocity, and the radius when the width of the axiallysymmetric region is about equal to the width of the ingot, a similarexpression may be given when the width is less than equal to the radiusof the ingot. More specifically, if the width of the axially symmetricregion is less than equal to the radius of the ingot, then R (denotingthe radius of the ingot) in Equation (e) is replaced with (R-R_(v))wherein R_(v) represents the width of the vacancy dominated sore asdetermined by measuring from the central axis radially outward to theV/I boundary. Accordingly, the radius of the ingot has been replaced bythe width of the self-interstitial dominated region, due at least inpart to the fact that the diffusion distance hag decreased. A similarrelationship may be provided when the focus is upon the vacancydominated region as the region which is substantially defect free,wherein R is replaced with (R-R₁), R₁ representing the width of theinterstitial dominated ring.

[0111] It is to be further noted that while the above describedrelationships are based on the assumption that G₀ is constant across theradius of the ingot, generally speaking, the same is true for thesituation wherein G₀ varies radially. More specifically, radialvariations in G₀ are acceptable when growth conditions are controlled toensure self-interstitials predominate (excluding of course a core ofvacancy-dominated material which may be annihilated by recombinationwith interstitials) because, given sufficient time, out diffusion ofself-interstitials acts to compensate for any variation in the initialconcentration of intrinsic point defects. While significantly longperiods of time would be required, the same is essentially true whenvacancies predominate, as well.

[0112] While the robust nature, or flexibility, of the present processallows for radial variations in G₀, it should also be noted that thepresent process allows for axial variations in G₀, as well. Morespecifically, changes in the initial concentration of intrinsic pointdefects (i.e., the concentration after the ingot has cooled to about1300° C., or even about 1325° C.) generally near the central axis (wherediffusion distance is typically the greatest) may occur from one axialposition to the next as a result of changes in G₀, as well as v.Accordingly, the effects of outdiffusion can be utilized to offset thesechanges in defect concentration regardless of the cause.

[0113] Referring now to FIGS. 10 and 11, the relationship between thenormalized value S of the threshold interstitial concentration (i.e.,the ratio of the concentration C at the temperature T_(cr) at whichagglomerations might otherwise form over the concentration C_(lm) at thetime of solidification) and the ratio of the critical value of G₀ overthe actual value of G₀ is plotted. It is to be noted that experienceto-date suggests this normalized value of the threshold concentration isless than about 0.01, possibly about 0.005; that is, the formation ofagglomerated self-interstitial intrinsic point defense can be avoidedprovided the normalized concentration remains below this value.

[0114] Referring now to FIG. 10 and corresponding Table II, below, therelationship between changes in (G₀)_(cr)/G₀ and the normalizedinterstitial concentration may be observed for a single crystal siliconingot having a nominal diameter of about 150 mm, for a number ofdifferent dwell lengths. From this plot, it can be seen that as thedwell length continues to increase (moving right to left from curve 1 tocurve 7), more and more of the curve is below the estimated thresholdconcentration of about 0.005, thus allowing for greater variability inG₀. Specifically, as can be seen from Table II, for a constant pull rate(about 0.28 mm/min. here) a “window” of about 30% variability isafforded G₀ by a dwell length which is within about a typical crystallength (i.e., less than about 100 cm). TABLE II Curve L_(dw) delta (G₀)_(cr)/G₀ 1 30 cm  5% 2 40 cm  7% 3 50 cm 10% 4 60 cm 13% 5 70 cm 18% 680 cm 24% 7 90 cm 31%

[0115] A similar observation can be made from FIG. 11 and correspondingTable III, below, for a single crystal silicon ingot having a nominaldiameter of about 200 mm. Once again it can be seen from the plot thatas the dwell length increases, more of the curve is below the estimatedthreshold concentration of about 0.005, thus allowing for greatervariability in G₀. However, as Table III indicates, the impact Of thesame increase in dwell length is lessened here, due to the increase indiffusion distance necessary to effectively suppress the interstitialconcentration and thus prevent the formation of agglomerated defects.TABLE III Curve L_(dw) delta (G₀) _(cr)/G₀ 1 30 cm  4% 2 40 cm  5% 3 50cm  6% 4 60 cm  8% 5 70 cm 10% 6 80 cm 12% 7 90 cm 15%

[0116] It is to be noted that the calculated width of the “window” ofvalues for G₀ which enable the formation of agglomerated defects to beprevented is at least in part dependent upon the estimated value for S,as well as the assumed interstitial diffusively value D₁ (which in thepresent examples is estimated to be about 2×10⁻⁴ cm²/sec.). However, thequalitative results presented here are believed to be the same within areasonable range of values for S and D₁.

[0117] It is to be further noted that, as can be observed from FIGS. 10and 11, unlike the case discussed above wherein G₀ remained constantwhile v was allowed to vary (see, e.g., FIGS. 4 and 5), the curvespresented here do not reach a maximum. Stated another way, when v isallowed to vary, do the dwell length continues to increase, eventually apoint is reached where the entire curve falls below the criticalconcentration. In contrast, when G₀ is allowed to vary, no such point isreached; that is, the G₀ “window” of acceptable values does not becomecomplete open as it does when v is allowed to vary.

[0118] Additionally, as can be observed from FIGS. 10 and 11, the curvescontinue on an upward slope as G₀ increases. In contrast, when v isallowed to vary, the curves initially have an upward slope but then,after reaching a plateau, the curves change to a downward slope. Theshape of the v variation curves is due to the offsetting effect of adecrease in v. More specifically, while a decrease in v cause theconcentration if interstitials to increase, the time for diffusion alsoincreases. At some point, the effects of diffusion outweigh the increasein concentration. No such offsetting effect is present when G₀ is thesource of variation, as FIGS. 10 and 11 indicate.

[0119] Definitions

[0120] As used herein, the following phrases or terms shall have thegiven meanings; “agglomerated intrinsic point defects” mean defectscaused (i) by the reaction in which vacancies agglomerate to produceD-defects, flow pattern defects, gate oxide integrity defects, crystaloriginated particle defects, crystal originated light point defects, andother such vacancy related defects, or (ii) by the reaction in whichself-interstitials agglomerate to produce dislocation loops andnetworks, and other such self-interstitial related defects;“agglomerated interstitial defects” shall mean agglomerated intrinsicpoint defects caused by the reaction in which silicon self-interstitialatoms agglomerate; “agglomerated vacancy defects” shall meanagglomerated vacancy point defects caused by the reaction in whichcrystal lattice vacancies agglomerate; “radius” means the distancemeasured from a central axis to a circumferential edge of a wafer oringot; “substantially free of agglomerated intrinsic point defects”shall mean a concentration of agglomerated defects which is less thanthe detection limit of these defects, which is currently about 10³defects/cm³ “V/I boundary” means the position along the radius of aningot or wafer at which the material changes from vacancy dominated toself-interstitial dominated; “vacancy dominated” and “self-interstitialdominated” mean material in which the intrinsic point defects arepredominantly vacancies or seif-interstitials, respectively; and,“(V/G₀)_(cr)” is intended to refer to the critical value of v/G₀, takinginto account the effects of vacancy or self-interstitial annihilation asa result of recombination as the ingot cools.

EXAMPLE

[0121] As the following Example illustrates, the present inventionaffords a process for preparing a single crystal silicon ingot whereinv/G₀ may vary, either radially or axially, as a result of changes in v,G₀, or both. By utilizing the effects of controlled cooling and theoutdiffusion of intrinsic point defects, the present process thusaffords greater flexibility in the preparation of single crystal siliconsubstantially free of agglomerated intrinsic point defects, such thatmaintaining the value of v/G₀ within a narrow, “target” range of valuesis no longer necessary it should be noted, however, that the Examplesets forth only approach and one get of conditions that may be used toachieve the desired result. Accordingly, it should not be interpreted ina limiting sense.

Example

[0122] Two 200 mm crystal ingots were crown in a crystal puller capableof producing a substantially defect-free axially symmetric region ofinterstitial dominated material having a width and length essentiallyequal to the radius and length, respectively, of the constant diameterportion of the ingots. Such an axially symmetric region may be achievedin the given crystal puller when the ingots are grown at the ratedepicted by the dashed line in FIG. 3A (hereinafter, the “defect-free”growth rate curve).

[0123] The two crystals were grown at the same target growth rate,depicted in FIG. 3A as a continuous line, with the growth rate beingreported as a normalized growth rate (i.e., the actual growth raterelative to the critical growth rate, typically expressed as a ratio ofv/v_(cr)). As depicted, these ingots were initially grown for a periodof time at a rate which was in excess of the “defect-free” growth ratecurve, then for a period of time at a rate which was less than the“defect-free” growth rate curve, and then again for a period of time ata rate in excess of the “defect-free” growth rate curve.

[0124] The first ingot (87GEX) was allowed to cool naturally in thecrystal growth chamber upon completion of the growth of the ingot. Thesecond ingot (87GEW), however was not allowed to cool naturally in thecrystal growth chamber; instead, upon completion of the growth of theingot, the heaters in the hot zone of the crystal puller remained on andthe ingot was held for 30 hours in the pull chamber.

[0125] It is to be noted that, with regard to the second ingot (87GEW),a non-uniform temperature profile wag employed, the profile beingestablished such that regions of the ingot more than about 400 mm fromthe seed end were held at a temperature in excess of about 1,050° C.while regions less than about 400 mm from the seed end were held at atemperature less than about 1,050° C. during this period.

[0126] The ingots were sliced longitudinally along the central axisrunning parallel to the direction of growth, and then further dividedinto sections, each about 2 mm in thickness. Using a copper decorationtechnique (as described in PCT/US98/07365 and PCT/US98/07304), followedby a standard defect delineating etch, the samples were visuallyinspected for the presence of precipitated impurities; those regionswhich were free of such precipitated impurities corresponded to regionswhich were free of agglomerated interstitial defects. Photographs werethen taken of the sections of each crystal and assembled to show theresults for each crystal from seed to tail end. The set of photographsfor the first, naturally-cooled ingot (87GEX) are depicted in FIG. 3Band the set of photographs for the second, held ingot (87GEW) aredepicted in FIG. 3C.

[0127] Referring now to FIGS. 3A, 3B, and 3C, it can be seen that thenaturally-cooled ingot (87GEX) contains agglomerated vacancy defectsfrom 0 to about 393 mm, no agglomerated intrinsic point defects fromabout 393 mm to about 435 mm, agglomerated intrinsic point defects fromabout 435 mm to about 513 mm, no agglomerated intrinsic point defectsfrom about 513 mm to about 557 mm, and agglomerated vacancy defects from557 mm to the end of the crystal. These correspond to the regions above,within and below the defect-free growth conditions for this hot zone.The held ingot (87GEW) contains agglomerated vacancy defects from 0 toabout 395 mm, no agglomerated intrinsic point defects from about 395 mmto about 584 mm, and agglomerated vacancy defects from about 584 mm tothe end of the crystal. The most significant difference between the twoingots, therefore, occurs in the region from about 435 mm to about 513mm in which the naturally-cooled ingot (87GEX) contains agglomeratedintrinsic point defects whereas the held ingot (87GEW) does not. Duringthe holding period, the concentration of self-interstitial silicon atomsin the held ingot (87GEW) is suppressed by additional diffusion of theself-interstitial atoms to the surface of the ingot and vacancydominated regions and thus, critical supersaturation and theagglomeration reaction for interstitial atoms is avoided subsequent tocrystal solidification. In the naturally cooled ingot, however,insufficient time is allowed for additional diffusion to the surface andvacancy dominated regions and, as a result, the system becomescritically supersaturated in silicon self-interstitial atoms and anagglomeration reaction occurs.

[0128] It is to be noted that these ingots therefore illustrate that,given sufficient amounts of time and no sufficiently high temperatures,virtually any amount Of silicon self-interstitial atoms can beoutdiffused to the surface.

[0129] It is to be further noted that the “defect-free” growth ratecurve depicted in FIG. 3A falls within a range of crystal growth rateswhich provide fully agglomerated intrinsic affect-free material undernatural cooling conditions for this crystal puller configuration.Referring now to Table IV below, it can be seen that even under naturalcooling conditions for this hot zone configuration, There is a range Ofcrystal growth rates between the growth rate (P_(v)) at whichagglomerated vacancy defects form and the growth rate (P_(I)) at whichagglomerated intrinsic point defects form; this range is at least ±5% ofthe average of P_(v), and P_(I). When the residence time of the growncrystal at temperatures in excess of about 1,050° C. is increased, thisrange is increased further with the range being, for example, at least±7.5%, at least ±10%, or even at least ±15% of the average of P_(v) andP_(I) (for example, for crystal 87GEW the residence was sufficientlygreat that, P_(I), was not achieved and thus, P_(I) for this crystal wasless than the lowest pull rate achieved). TABLE IV Tran- positionNormalized Window % variation sition mm Pull rate, V V_ave (DV)100(DV/Vave) 87GEX V-P 393 0.251 P-I 435 0.213 0.232017 0.03865546 16.66I-P 523 0.209 P-V 557 0.249 0.22937 0.0402521 17.55 87GEW V-P 395 0.246P* 465 0.196 0.221008 0.05042017 22.81 P* 465 0.196 P-V 584 0.2710.233193 0.07478992 32.07

[0130] For a given crystal puller and hot zone configuration, it may beassumed that the axial temperature gradient, G₀, is approximatelyconstant over relatively short distances, such as the transition rangeswhich occur here. An a consequence, a change in the crystal growth rateleads to a proportional change in v/G₀, and thus, the initialconcentration of vacancies and silicon self-interstitial atoms. Ingeneral, however, the value of v/G₀ at the center ingot is the mostcritical value since it is the farthest distance from the surface.Therefore, the results of this example demonstrate that the increase inpull rate variations achieved through increased dwell times attemperatures greater than about 1000° C. implies those correspondingvariations in v/G₀ may occur at any point along the radius of thecrystal. In other words, radial variation of v/G₀ is irrelevant andthus, for example, may exceed (at any radial position) 10%, 15% or moreof the value of v/G₀ at the center of the ingot.

[0131] As can be seen from the above data, by means of controlling thecooling rate, the concentration of intrinsic point defects may besuppressed by allowing more time for these defects to diffuse to regionswhere they may be annihilated. An a result, the formation ofagglomerated intrinsic point defects is prevented within a significantportion of the constant diameter portion of the single crystal siliconingot. In view of the above, it will be seen that the several objects ofthe invention are achieved.

[0132] As various changes could be made in the above compositions andprocesses without departing from the scope of the invention, it isintended that all matters contained in the above description areinterpreted as illustrative and not in a limiting sense.

What is claimed is:
 1. A process for growing a single crystal siliconingot having a central axis, a seed-cone, an end-cone, a constantdiameter portion between the seed-cone and the end-cone, and an ingotsegment which comprises a fraction of the Constant diameter portion andwhich is substantially free of agglomerated intrinsic point defects, theprocess comprising: Allowing the ratio v/G₀ to vary as a function of thelength of the ingot segment as the ingot is grown, with v/G₀ beingallowed to vary between a minimum value, (v/G₀)_(min), and a maximumvalue, (v/G₀)_(max), where v is the growth velocity and G₀ is theaverage axial temperature gradient between the temperature ofsolidification and about 1300° C. at the central axis, with (v/G₀)_(min)being no more than about 95% of (v/G₀)_(max); and, cooling the ingotsegment from the temperature of solidification to a temperature betweenabout 1050° C. and about 900° C. over a dwell time, t_(dw), which insufficient to prevent the formation of agglomerated intrinsic pointdefects within the segment.
 2. The process of claim 1 wherein the ingotsegment has a length which is at least about 40% of the length of theconstant diameter portion.
 3. The process of claim 1 wherein the ingotsegment has a length which is at least about 80% of the length of theconstant diameter portion.
 4. The process of claim 1 wherein the ingotsegment has a length which is at least about 90% of the length of theconstant diameter portion.
 5. The process of claim 1 wherein the ingothas a nominal diameter of about 150 mm and t_(dw) is at least about 10hours.
 6. The process of claim 1 wherein the ingot has a nominaldiameter of about 200 mm and t_(dw) is at least about 20 hours.
 7. Theprocess of claim 1 wherein the ingot has a nominal diameter of greaterthan 200 mm and t_(dw) is at least about 40 hours.
 8. The process ofclaim 1 wherein (v/G₀)_(min) is no more than about 90% of (v/G₀)_(max).9. The process of claim 8 wherein the ingot segment has a length whichis at least about 40% of the length of the constant diameter portion.10. The process of claim 8 wherein the ingot segment has a length whichis at least about 80% of the length of the constant diameter portion.11. The process of claim 8 wherein the ingot segment has a length whichis at least about 90% of the length of the constant diameter portion.12. The process of claim 8 wherein the ingot has a nominal diameter ofabout 150 mm and t_(dw) is at least about 10 hours.
 13. The process ofclaim 8 wherein the ingot has a nominal diameter of about 200 mm andt_(dw) is at least about 20 hours.
 14. The process of claim 8 whereinthe ingot has a nominal diameter of greater than 200 mm and t_(dw) is atleast about 40 hours.
 15. The process of claim 1 wherein (v/G₀)_(min) isno more than about 80% of (v/G₀)_(max).
 16. The process of claim 15wherein the ingot segment has a length which is at least about 40% ofthe length of the constant diameter portion.
 17. The process of claim 15wherein the ingot segment has a length which is at least about 80% ofthe length of the constant diameter portion.
 18. The process of claim 15wherein the ingot segment has a length which is at least about 90% ofthe length of the constant diameter portion.
 19. The process of claim 15wherein the ingot has a nominal diameter of about 150 mm and t_(dw) isat least about 10 hours.
 20. The process of claim 15 wherein the ingothas a nominal diameter of about 200 mm and t_(dw) is at least about 20hours.
 21. The process of claim 15 wherein the ingot has a nominaldiameter of greater than 200 mm and t_(dw) is at least about 40 hours.22. A process for growing a single crystal silicon ingot having acentral axis, a seed-cone, an end-cone, a constant diameter portionbetween the seed-cone and the end-cone having a circumferential edge anda radius extending from the central axis to the circumferential edge,the ingot being characterized in that, after the ingot is grown from asilicon melt and cooled from the solidification temperature inaccordance with the Czochralski method, the constant diameter portioncontains an axially symmetric region which is substantially free ofagglomerated intrinsic point defects, the process comprising;controlling a growth velocity, v, and an average axial temperaturegradient, G₀, during the growth of the constant diameter portion of theingot over a temperature range from solidification to about 1300° C.;and, the cooling rate of the axially symmetric region, the axiallysymmetric region cooling from a first temperature, T₁, which is betweenabout 1400° C. and about 1300° C., to a second temperature, T₂, which isbetween about 1050° C. and about 900° C., with the rate of temperaturedecrease from T₁ to T₂being controlled such that at each intermediatetemperature, T_(int), between T₁ and T₂, the axially symmetric regionhas a concentration of silicon self-interstitial intrinsic point defectswhich is less than a critical concentration at which agglomeratedintrinsic point defects form, wherein the axially symmetric region has awidth, as measured radially from the circumferential edge toward thecentral axis, which is at least about 30% of the width of the constantdiameter portion of the ingot and has a length which is at least about20% of the length of the constant diameter portion of the ingot.
 23. Theprocess of claim 22 wherein the axially symmetric region has a widthwhich is at least about 60% of the width of the constant diameterportion.
 24. The process of claim 22 wherein the axially symmetricregion has a width which is at least about 95% of the width of theconstant diameter portion.
 25. The process of claim 22 wherein theaxially symmetric region has a width which is about equal to the widthof the constant diameter portion.
 26. The process of claim 22 whereinthe axially symmetric region has a length which is at least about 40% ofthe length of the constant diameter portion.
 27. The process of claim 26wherein the axially symmetric region has a width which is at least about60% of the width of the constant diameter portion.
 28. The process ofclaim 26 wherein the axially symmetric region has a width which is atleast about 95% of the width of the constant diameter portion.
 29. Theprocess of claim 26 wherein the axially symmetric region has a widthwhich is about equal to the width of the constant diameter portion. 30.The process of claim 22 wherein the axially symmetric region has alength which is at least about 80% of the length of the constantdiameter portion.
 31. The process of claim 22 wherein the average 0.1°C./minute and about 3° C./minute.
 32. The process of claim 22 whereinthe average rate of temperature decrease is between about 0.1° C./minuteand about 1° C./minute.
 33. The process of claim 22 wherein the averagerate of temperature decrease is between about 0.1° C./minute and about0.5° C./minute.